Within-basket recommendation reduces the exploration time of users, where the users intention of the basket matters. The intent of a shopping basket can be retrieved from both user-item collaborative filtering signals and multi-item correlations. By defining a basket entity to represent the basket intent, we can model this problem as a basket-item link prediction task in the User-Basket-Item~(UBI) graph. Previous work solves the problem by leveraging user-item interactions and item-item interactions simultaneously. However, collectivity and heterogeneity characteristics are hardly investigated before. Collectivity defines the semantics of each node which should be aggregated from both directly and indirectly connected neighbors. Heterogeneity comes from multi-type interactions as well as multi-type nodes in the UBI graph. To this end, we propose a new framework named textbf{BasConv}, which is based on the graph convolutional neural network. Our BasConv model has three types of aggregators specifically designed for three types of nodes. They collectively learn node embeddings from both neighborhood and high-order context. Additionally, the interactive layers in the aggregators can distinguish different types of interactions. Extensive experiments on two real-world datasets prove the effectiveness of BasConv. Our code is available online at https://github.com/JimLiu96/basConv.
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